C₅₉×#8639 #28420748

order	15104
nilpotency class	3
isoclinism	isoclinic class of #8626
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₅₉×#8639

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅₉	#380
commutator	C₂²×C₄	C₂²×C₄×C₅₉
Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
prime radical	C₂³×C₅₉	#117
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

336 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 7552

A minimal faithful permutation representation — 3 generators on 91 points:

(1,2,6,9,7,4,5,15)(3,10,13,11,14,16,12,8)(18,22)(19,26)(20,23)(25,30)(27,28)(29,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3,6,13,7,14,5,12)(2,8,15,16,4,11,9,10)(17,18,23,30,21,25,20,22)(19,24,26,31,28,32,27,29);(1,4)(2,7)(3,11)(5,15)(6,9)(8,14)(10,13)(12,16)(17,19,21,28)(18,24,25,32)(20,27,23,26)(22,29,30,31)

Conjugacy classes & character table

2360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1627);